This invention relates to a control system which utilizes the state of chaos and can be widely applied to the automatic control of a system exhibiting a chaotic behavior.
The manner of control based on the OGY algorithm or the SOGY algorithm is one form of control technology utilizing chaos. The OGY algorithm refers to an algorithm in which, when a system to be controlled is located in the neighborhood of an unstable periodic point on the Poincare surface of section in the phase space, a tiny perturbation is applied to the system so that the system can be stabilized at this periodic point. (Refer to, for example, Phys. Rev. Lett., 64, 1196-1199 (1990)). The periodic point referred to above is a point where the orbit of the system in its periodic state pierces the Poincare surface of section. The OGY algorithm assumes that the Poincare map is linearly dependent on the control parameter p. Therefore, the control parameter p can be adjusted in a finite region I.sub.p expressed as I.sub.p (= p.sub.min, p.sub.max !, that is, p.sub.min .ltoreq.p.ltoreq.p.sub.max). As a result, in order that the OGY algorithm can effectively work, a restriction is imposed according to which the system must lie within a certain region I.sub.t. On the other hand, the SOGY algorithm is such that a tiny perturbation is applied to the system so that the state of the system can be quickly shifted toward a desired state (a target) on the orbit of chaos. (Refer to, for example, Phy. Rev. Lett., 65, 3215-3218 (1990)).
It was considered hitherto that the combination of the OGY algorithm and the SOGY algorithm could attain the purpose of desired quick control. (Refer to, for example, J. Phys. Chem., 95, 4957-4959 (1991)).